In March of 1997 Bob Goodwin posted on a multiage listserve a description of the eclectic math program that he uses. It is another good way to "do math" in a multiage setting, especially when trying to balance district curriculum edicts with the flexibility and choice needed in a multiage classroom. With his permission I have reposted it here.
My math classes are a combination of different approaches:
For bellwork I have three sets of problems on the board (A,B, and C). The "A" set is what all third and fourth grade students are expected to start with. The "B" set is for all fifth and sixth grade students to start with. The "C" set is for challenge problems. Each set is made up of 3 - 5 problems.... usually computational, but also story problems. Each student gets a small piece of paper (usually a quarter of a 8.5x11 inch piece) and starts to solve the problems in their first set. When they finish they may get another sheet to solve the next set, and so on. We correct all sets as a class so that all students participate and hear how the others problem solve. Sort of like daily oral math, but we don't do it every day. Each student is responsible for making sure they make any corrections that need to be made when we solve as a class. Each piece of paper then becomes a ticket in a drawing for small prizes in a drawing I have every two weeks. The only requirement to win in the drawing is that the student must have corrected any mistakes they originally made or I pick another piece of paper. I give away pencils, erasers... that sort of stuff.
The benchmark tests are a work in progress, but try to cover in a sequential way, major concepts in math. Each student takes one or two each week to check on progress, and I often have older students giving "mini-lessons" to their younger peers. This works particularly well with many of my second language asian students.
Each week I use material from grade level text books as resources for learning and practice. I often will assign particular pages for homework, and then have have the kids meet in "grade level" groups to go over and correct their homework together. Each week I pick different kids to facilitate homework correction, and I try to float around between groups to check on progress, but often spend most of my time working with the third graders. This is the only grade specific work I do. Our district only gives me text books for what ever numbers and grades I have in my room.
I also have enough computers in my room to have some children practice while I work with specific children in groups or alone on specific math needs.
I use a cash economy in my room where each student is paid for quality work (our own class money which I print up). There are also elected classroom jobs or offices. Right now I am trying out decreasing the number of classroom jobs and having the class elect "managers" for different areas like library, bulletin boards, Banker, etc.. I am giving each manager a budget to "hire" other students to help them keep their area ship-shape. Classroom accounts are kept by the banker, and money is spent in monthly auctions, movies at lunch time, computer games at lunch, etc....
In addition to the above my school district has one major math performance assessment each year. This year we did an assessment where each child was to plan a trip to a country of their choice, research the climate and sights to see, and then pick out and buy appropriate clothing from catalogs with a $300 budget.
My school has required monthly open-ended math assessments which every child does at our school, K - 6, and which are scored on a 6 point rubric and recorded into a data base in a very disaggregated way.